It is a well known fact that all non-opaque materials have a wavelength dependent index of refraction. Additionally, every material has a characteristic dispersion, which is the variation of the refractive index with wavelength. The index of refraction may therefore be denoted n(λ), where n is the index of refraction and is a pure number and λ is the wave length and is measured in units of length. FIG. 1 shows the wavelength dependency of the index of refraction in polycarbonate, which is a popular material for spectacles lenses.
For calculations of optical powers in spectacles lenses, professionals usually use a refraction index which correlates to a wavelength of about 585 nm. In the electromagnetic spectrum, this wavelength corresponds to the yellow color emitted by sodium. This usual refraction index may be denoted n*=n(585). For polycarbonate, n* has a value of about 1.585.
In most cases when a lens is to be processed for a certain prescription, one of surfaces is already in its finished topography and no surface processing needs to be applied on it (usually this is the front surface) and the other surface needs to be milled ground or lathed to a new topography so that at the end of the process the two surfaces combined give optics that fit the patient's Rx (prescription). There are many ways for calculating the back surface topography of the lens to fit the Rx. The simplest approximation is called the thin lens approximation or Lensmaker's equation:
                              1                      r            b                          =                                                            (                                                      n                    *                                    -                  1                                )                            ⁢                              1                                  r                  f                                                      -                          1              f                                                          n              *                        -            1                                              Equation        ⁢                                  ⁢        1            where n* is the refraction index of yellow light (585 nm), f is the required focal length of the lens (given by the Rx prescription), rb is the radius of curvature of the back surface of the lens and rf is the radius of curvature of the front surface. Equation 1 provides the back surface radius that fits an Rx given the radius of a spherical front surface and the required focal length according to the Rx, assuming the lens is negligibly thin. A further constraint is that the lens optics is paraxial. For example, if the lens is strongly tilted or has a strong prism, other and usually more complicated models have to be used. If one wants to design a progressive lens having a power distribution and a residual cylinder distribution, one would have to employ optimization algorithms. Substantially all of these methods use the index of refraction as a parameter in their calculations.
It will be appreciated that for simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn to scale. For example, the dimensions of some of the elements may be exaggerated relative to other elements for clarity. Further, where considered appropriate, reference numerals may be repeated among the figures to indicate corresponding or analogous elements.